The problem of topology control in multi-rate mobile ad hoc networks is studied and a multi-rate aware topology control algorithm (MATC) is proposed in the paper. MATC fully takes the inherent multi-rate property of wireless network into account. It removes some low rate links while preserving the connectivity of the network. On the basis of MATC, on-demand routing protocols can find the optimal route in one-hop range. Extensive simulations show that MATC can significantly improve the network throughput.